# Barron's AP calculus

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Publication date
2010

Topics
Calculus, Advanced placement programs (Education), College entrance achievement tests, Advanced placement programs (Education), Calculus, College entrance achievement tests

PublisherHauppauge, NY : Barron's

Collectioninlibrary; printdisabled; internetarchivebooks; china

Digitizing sponsorKahle/Austin Foundation

ContributorInternet Archive

LanguageEnglish

Includes index

System requirements for CD-ROM: PC with Windows Intel Pentium II 450 MHz or faster processor, 128 MB of RAM, 1024 x 768 display resolution, Windows 2000, XP, Vista, CD-ROM player ; Macintosh with PowerPC G3 500 MHz or faster, 128 MB of RAM, 1024 x 768 display resolution, Mac OS X v.10.1 through 10.4, CD-ROM player

Introduction -- Courses -- Topics that may be tested on the calculus AB exam -- Topics that may be tested on the calculus BC exam -- Examinations -- Graphing calculator: using your graphing calculator on the AP exam -- Grading the examinations -- CLEP calculus examination -- This review book -- Diagnostic Tests -- Calculus AB -- Calculus BC -- Topical Review And Practice -- Functions -- Definitions -- Special functions -- Polynomial and other rational functions -- Trigonometric functions -- Exponential and logarithmic functions -- Parametrically defined functions -- Practice exercises -- Limits And Continuity -- Definitions and examples -- Asymptotes -- Theorems on limits -- Limit of a quotient of polynomials -- Other basic limits -- Continuity -- Practice exercises -- Differentiation -- Definition of derivative -- Formulas -- Chain rule; the derivative of a composite function -- Differentiability and continuity -- Estimating a derivative -- Numerically -- Graphically -- Derivatives of parametrically -- Defined functions -- Implicit differentiation -- Derivative of the inverse of a function -- Mean value theorem -- Indeterminate forms and L'Hopitals' rule -- Recognizing a given limit as a derivative -- Practice exercises -- Applications of differential calculus -- Slope; critical points -- Tangents and normals -- Increasing and decreasing functions -- Case 1: Functions with continuous derivatives -- Case 2: Functions whose derivatives have discontinuities -- Maximum, minimum, and inflection points: definitions -- Maximum, minimum, and inflection points: curve sketching -- Case 1: Functions that are everywhere differentiable -- Case 2: Functions whose derivatives may not exist everywhere -- Global maximum or minimum -- Case 1: Differentiable functions -- Case 2: Functions that are not everywhere differentiable -- Further aids in sketching -- Optimization: problems involving maxima and minima -- Relating a function and its derivatives graphically -- Motion along a line -- Motion along a curve: velocity and acceleration vectors -- Tangent-line approximations -- Related rates -- Slope of a polar curve -- Practice exercises -- Antidifferentiation -- Antiderivatives -- Basic formulas -- Integration by partial fractions -- Integration by parts -- Applications of antiderivates; differential equations -- Practice exercises -- Definite Integrals -- Fundamental theorem of calculus (FTC); definition of definite integral -- Properties of definite integrals -- Integrals involving parametrically defined functions -- Definition of definite integral as the limit of a sum: the fundamental theorem again -- Approximations of the definite integral: Riemann sums -- Using rectangles -- Using trapezoids -- Comparing approximating sums -- Graphing a function from its derivative; another look -- Interpreting 1n x as area -- Average value -- Practice exercises -- Applications Of Integration To Geometry -- Area -- Area between curves -- Using symmetry -- Volume -- Solids with known cross sections -- Solids of revolution -- Arc length -- Improper integrals -- Practice exercises -- Further Applications Of Integration -- Motion along a straight line -- Motion along a plane curve -- Other applications of Riemann sums -- FTC: definite integral of a rate is net change -- Practice exercises -- Differential Equations -- Basic definitions -- Slope fields -- Euler's method -- Solving first-order differential -- Equations analytically -- Exponential growth and decay -- Case 1: Exponential growth: dy_dt=ky -- Case 2: Restricted growth: dy_dt=k(A-y) -- Case 3: Logistic growth: dy_dt=ky(A-y) -- Practice exercises -- Sequences And Series -- Sequences of real numbers -- Infinite series -- Definitions -- Theorems about convergence or divergence of infinite series -- Test for convergence of infinite series -- Tests for convergence of nonnegative series -- Alternating series and absolute convergence -- Power series -- Definition; convergence -- Functions defined by power series -- Finding a power series for a function: Taylor and Maclaurin series -- Approximating functions with Taylor and Maclaurin polynomials -- Taylor's formula with remainder; Lagrange error bound -- Computations with power series -- Power series over complex numbers -- Practice exercises -- Miscellaneous Multiple-Choice Practice Questions -- Miscellaneous Free-Response Practice Exercises -- AB Practice Examinations -- AB one -- AB two -- AB three -- BC Practice Examinations -- BC one -- BC two -- BC three -- Appendix: Formulas and theorems for reference -- Index

Overview: Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Prospective test takers will find four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. The manual also provides a detailed 10-chapter review covering topics for both exams. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators

System requirements for CD-ROM: PC with Windows Intel Pentium II 450 MHz or faster processor, 128 MB of RAM, 1024 x 768 display resolution, Windows 2000, XP, Vista, CD-ROM player ; Macintosh with PowerPC G3 500 MHz or faster, 128 MB of RAM, 1024 x 768 display resolution, Mac OS X v.10.1 through 10.4, CD-ROM player

Introduction -- Courses -- Topics that may be tested on the calculus AB exam -- Topics that may be tested on the calculus BC exam -- Examinations -- Graphing calculator: using your graphing calculator on the AP exam -- Grading the examinations -- CLEP calculus examination -- This review book -- Diagnostic Tests -- Calculus AB -- Calculus BC -- Topical Review And Practice -- Functions -- Definitions -- Special functions -- Polynomial and other rational functions -- Trigonometric functions -- Exponential and logarithmic functions -- Parametrically defined functions -- Practice exercises -- Limits And Continuity -- Definitions and examples -- Asymptotes -- Theorems on limits -- Limit of a quotient of polynomials -- Other basic limits -- Continuity -- Practice exercises -- Differentiation -- Definition of derivative -- Formulas -- Chain rule; the derivative of a composite function -- Differentiability and continuity -- Estimating a derivative -- Numerically -- Graphically -- Derivatives of parametrically -- Defined functions -- Implicit differentiation -- Derivative of the inverse of a function -- Mean value theorem -- Indeterminate forms and L'Hopitals' rule -- Recognizing a given limit as a derivative -- Practice exercises -- Applications of differential calculus -- Slope; critical points -- Tangents and normals -- Increasing and decreasing functions -- Case 1: Functions with continuous derivatives -- Case 2: Functions whose derivatives have discontinuities -- Maximum, minimum, and inflection points: definitions -- Maximum, minimum, and inflection points: curve sketching -- Case 1: Functions that are everywhere differentiable -- Case 2: Functions whose derivatives may not exist everywhere -- Global maximum or minimum -- Case 1: Differentiable functions -- Case 2: Functions that are not everywhere differentiable -- Further aids in sketching -- Optimization: problems involving maxima and minima -- Relating a function and its derivatives graphically -- Motion along a line -- Motion along a curve: velocity and acceleration vectors -- Tangent-line approximations -- Related rates -- Slope of a polar curve -- Practice exercises -- Antidifferentiation -- Antiderivatives -- Basic formulas -- Integration by partial fractions -- Integration by parts -- Applications of antiderivates; differential equations -- Practice exercises -- Definite Integrals -- Fundamental theorem of calculus (FTC); definition of definite integral -- Properties of definite integrals -- Integrals involving parametrically defined functions -- Definition of definite integral as the limit of a sum: the fundamental theorem again -- Approximations of the definite integral: Riemann sums -- Using rectangles -- Using trapezoids -- Comparing approximating sums -- Graphing a function from its derivative; another look -- Interpreting 1n x as area -- Average value -- Practice exercises -- Applications Of Integration To Geometry -- Area -- Area between curves -- Using symmetry -- Volume -- Solids with known cross sections -- Solids of revolution -- Arc length -- Improper integrals -- Practice exercises -- Further Applications Of Integration -- Motion along a straight line -- Motion along a plane curve -- Other applications of Riemann sums -- FTC: definite integral of a rate is net change -- Practice exercises -- Differential Equations -- Basic definitions -- Slope fields -- Euler's method -- Solving first-order differential -- Equations analytically -- Exponential growth and decay -- Case 1: Exponential growth: dy_dt=ky -- Case 2: Restricted growth: dy_dt=k(A-y) -- Case 3: Logistic growth: dy_dt=ky(A-y) -- Practice exercises -- Sequences And Series -- Sequences of real numbers -- Infinite series -- Definitions -- Theorems about convergence or divergence of infinite series -- Test for convergence of infinite series -- Tests for convergence of nonnegative series -- Alternating series and absolute convergence -- Power series -- Definition; convergence -- Functions defined by power series -- Finding a power series for a function: Taylor and Maclaurin series -- Approximating functions with Taylor and Maclaurin polynomials -- Taylor's formula with remainder; Lagrange error bound -- Computations with power series -- Power series over complex numbers -- Practice exercises -- Miscellaneous Multiple-Choice Practice Questions -- Miscellaneous Free-Response Practice Exercises -- AB Practice Examinations -- AB one -- AB two -- AB three -- BC Practice Examinations -- BC one -- BC two -- BC three -- Appendix: Formulas and theorems for reference -- Index

Overview: Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Prospective test takers will find four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. The manual also provides a detailed 10-chapter review covering topics for both exams. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators

## Notes

The seams on page 185 and page 563 are too narrow to be scanned.

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Full catalog recordMARCXML

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